What Makes a Car Exchangeable?

Data Science 3 with R (STAT 301-3)

Author

ateam: Allie Tong & Alani Cox-Caceres

Github Repository

https://github.com/STAT301-3-2023SP/final-project-ateam

Data Overview

Our dataset consists of variables that describe cars in the used car market in Belarus on December 2, 2019. There are 38531 observations. Our target variable will be is_exchangeable, which is a factor variable that indicates TRUE if the used car can be exchanged with another car and FALSE if the used car cannot be exchanged with another car. There are 19 predictors, of which 1 is an integer, 5 are characters, 7 are numeric, and 6 are factors.

Goal

In this exploration, we’d like to examine ways to predict if the used cars will be exchangeable based on the variables that affect that outcome the most. This is a categorical prediction problem. We will to explore what factors make a car exchangeable by testing the predictor importance of various predictor variables.

Data Splitting and Resampling Plan

As seen above, our data was relatively unbalanced. To remedy this, we stratified our target variable, is_exchangeable, and used a 70/30 split for our training and testing data. For resampling, we used a cross-validation method. For the models that have shorter runtime, we will use 10 folds with 5 repeats. For the models that have longer runtime, we will use 5 folds and 3 repeats.

Feature Engineering

Missingness

# A tibble: 20 × 3
   variable          n_miss pct_miss
   <chr>              <int>    <dbl>
 1 engine_capacity       10   0.0260
 2 car_id                 0   0     
 3 manufacturer_name      0   0     
 4 model_name             0   0     
 5 transmission           0   0     
 6 color                  0   0     
 7 odometer_value         0   0     
 8 year_produced          0   0     
 9 engine_has_gas         0   0     
10 engine_type            0   0     
11 body_type              0   0     
12 has_warranty           0   0     
13 state                  0   0     
14 drivetrain             0   0     
15 price_usd              0   0     
16 is_exchangeable        0   0     
17 location_region        0   0     
18 number_of_photos       0   0     
19 up_counter             0   0     
20 duration_listed        0   0     

As seen above, there are no significant missing issues that could not be imputed and we found no significant missingness.

Variable Selection

Using the graphs above, we looked at the relationships between each of the predictors and the outcome variable. From looking at the relationships, we narrowed our relationship recipe to the predictors that displayed a relationship with the outcome variable. We plan to test if this improves model performance.

All of the feature engineering was done on a portion of the training set.

Recipe Building

Kitchen Sink

The kitchen sink recipe uses all of the variables in the dataset as predictors with is_exchangeable as the outcome variable. It will be used as a baseline to see if variable selection improves model performance.

We first had to use step_other() for model_name to deal with the large number of levels the variable had. Then, we dummy encoded all nominal predictors. After, we removed the variables with zero variance and centered and scaled all variables. Lastly, we used step_impute_knn() to impute missingess and step_corr() to remove variables that have large correlations with other ones.

There is a full kitchen sink recipe and a shortened kitchen sink recipe. The full kitchen sink recipe is performed on the training set of 26971 variables, while the shortened kitchen sink recipe is performed on a portion of the training set of 4045 variables. For tuning, the full kitchen sink recipe was used with 10 folds and 5 repeats, while the shortened kitchen sink recipe was used with 5 folds and 3 repeats.

Relationship Recipe

The relationship recipe uses the variables odometer_value, year_produced, engine_capacity, price_usd, number_of_photos, engine_has_gas, has_warranty, state, drivetrain, location_region, and manufacturer_name. These 11 variables showed possible relationships with the outcome variable is_exchangeable.

We first dummy encoded all nominal predictors. After, we removed the variables with zero variance and centered and scaled all variables. Lastly, we used step_impute_knn() to impute missingess and step_corr() to remove variables that have large correlations with other ones.

Similar to the kitchen sink model, there is a full relationship recipe and a shortened relationship recipe. The full relationship recipe is performed on the training set of 26971 variables, while the shortened relationship recipe is performed on a portion of the training set of 4045 variables. For tuning, the full relationship recipe was used with 10 folds and 5 repeats while the shortened relationship recipe was used with 5 folds and 3 repeats.

Importance Recipe

The importance recipe includes variables that had nonzero importance using random forest variable selection. After tuning the random forest model with the kitchen sink model, we looked at each variable’s importance. Displayed below is a table of the variables used and their importance in the random forest model.

Variable Importance
up_counter 788.6580490
duration_listed 617.7516304
odometer_value 503.0156605
number_of_photos 494.7243155
price_usd 481.0792365
car_id 449.8313468
year_produced 380.1960375
engine_capacity 274.4664908
location_region_Минская.обл. 92.8030975
state_new 46.8008940
has_warranty_TRUE. 46.5099238
transmission_mechanical 40.5825780
color_silver 40.3449514
engine_type_gasoline 39.6945323
color_grey 38.7421874
color_blue 38.3129939
color_other 38.2986681
body_type_sedan 36.9003696
body_type_universal 35.2781449
location_region_Могилевская.обл. 34.9461249
color_white 34.3796250
drivetrain_front 32.4351387
color_red 32.2518421
color_green 31.7374550
body_type_minivan 31.3655071
body_type_hatchback 31.1779763
location_region_Гомельская.обл. 30.8133901
manufacturer_name_Ford 30.0573848
manufacturer_name_Volkswagen 28.8299349
drivetrain_rear 28.4803476
location_region_Гродненская.обл. 27.9545426
location_region_Витебская.обл. 27.1022772
engine_has_gas_TRUE. 27.0698937
manufacturer_name_Audi 24.7320214
manufacturer_name_Renault 24.6318282
manufacturer_name_Mercedes.Benz 24.0924190
manufacturer_name_Mazda 23.5872786
state_owned 23.5273861
body_type_coupe 22.6612583
manufacturer_name_Skoda 22.2458098
manufacturer_name_Nissan 22.1907495
manufacturer_name_Opel 22.1527312
body_type_suv 21.9589566
manufacturer_name_Hyundai 21.6577733
manufacturer_name_BMW 21.5809222
manufacturer_name_Mitsubishi 20.9488206
manufacturer_name_Toyota 20.5626219
manufacturer_name_Volvo 20.4069748
body_type_minibus 20.2651658
manufacturer_name_Citroen 19.2354401
manufacturer_name_Fiat 18.0510079
model_name_other 17.8604464
color_violet 17.2447936
manufacturer_name_Honda 16.5131265
color_brown 16.2640276
manufacturer_name_Peugeot 16.1039589
manufacturer_name_Seat 15.3819134
body_type_van 15.3301251
manufacturer_name_Kia 14.7554339
body_type_liftback 12.9257577
manufacturer_name_Rover 12.5009331
color_yellow 12.3988095
manufacturer_name_Alfa.Romeo 11.6290891
manufacturer_name_Chevrolet 10.7032689
manufacturer_name_Chrysler 10.6656153
manufacturer_name_ВАЗ 9.2524306
manufacturer_name_Daewoo 8.3904637
manufacturer_name_Land.Rover 8.3290409
color_orange 7.6759916
manufacturer_name_Dodge 7.4537589
manufacturer_name_Suzuki 6.9912936
manufacturer_name_Lexus 6.4540726
manufacturer_name_Subaru 6.4213711
body_type_pickup 5.4805839
manufacturer_name_ГАЗ 5.2373095
manufacturer_name_Saab 5.1541324
manufacturer_name_Infiniti 4.8968141
manufacturer_name_Geely 4.6700420
manufacturer_name_Lancia 4.6201919
manufacturer_name_Iveco 4.5756640
manufacturer_name_Buick 4.3206742
manufacturer_name_Jeep 4.3122569
manufacturer_name_SsangYong 4.1300201
manufacturer_name_Mini 3.1768497
manufacturer_name_Dacia 2.7095752
manufacturer_name_LADA 2.6677245
manufacturer_name_Lincoln 2.6605691
manufacturer_name_Chery 2.5068993
manufacturer_name_Jaguar 2.2111715
manufacturer_name_Lifan 2.1178781
manufacturer_name_Great.Wall 1.8073144
manufacturer_name_Porsche 1.7981399
manufacturer_name_УАЗ 1.4300203
manufacturer_name_Cadillac 1.3759270
manufacturer_name_ЗАЗ 1.2604904
manufacturer_name_Pontiac 1.1377396
manufacturer_name_Москвич 0.8295686
engine_type_electric 0.5775882
body_type_limousine 0.4387792

As seen above, all of the variables used in the relationship recipe have importance. The importance recipe includes 6 more predictors than the relationship recipe.

We first dummy encoded all nominal predictors. After, we removed the variables with zero variance and centered and scaled all variables. Lastly, we used step_impute_knn() to impute missingess and step_corr() to remove variables that have large correlations with other ones.

We will not use the importance recipe for all of the models, but we will run the winning model with it to see if the importance recipe does better. For tuning, we will use 5 folds and 3 repeats on the entire training set.

Models Chosen + Parameters

The models we will be fitting are:

  • Null Model (to use as a baseline): A simple, non-informative model
    • Doesn’t have any main arguments
  • Random Forest Model: A model that creates a large number of decision trees, each independent of the others. It involves stratifying the predictor space into a number of simple regions. The predictions typically use the mean or mode response value in the region it belongs.
    • Tuning parameters:
      • min_n: The number of predictors that will be randomly sampled at each split when creating the tree models
      • mtry: The number of predictors that will be randomly sampled at each split when creating the tree models
        • Set an upper bound of 17 (max number of predictors a recipe would have)
  • Boosted Tree Model: A model that creates a series of decision trees forming an ensemble. Each tree depends on the results of previous trees. All trees in the ensemble are combined to produce a final prediction.
    • Tuning parameters: -min_n: The minimum number of data points in a node that is required for the node to be split further
      • mtry: The number (or proportion) of predictors that will be randomly sampled at each split when creating the tree models
        • Set an upper bound of 17 (max number of predictors a recipe would have)
      • learn_rate: The rate at which the boosting algorithm adapts from iteration-to-iteration
  • K Nearest Neighbors Model: A model that uses the K most similar data points from the training set to predict new samples
    • Tuning parameters:
      • neighbors: The number of neighbors to consider
  • Elastic Net Model: A model that uses linear predictors to predict multiclass data using the multinomial distribution
    • Tuning parameters:
      • penalty: A non-negative number representing the total amount of regularization
      • mixture: A number between zero and one (inclusive) giving the proportion of L1 regularization
        • Elastic net model interpolates lasso and ridge with 0 < mixture < 1
  • Logistic Regression Model: This model uses a linear combination of the predictors to calculate or predict the probability of an event occurring.
    • Tuning parameters:
      • penalty: A non-negative number representing the total amount of regularization
      • mixture: A number between zero and one (inclusive) giving the proportion of L1 regularization
        • mixture = 1: pure lasso model
        • mixture = 0: ridge regression model
  • SVM Poly Model: The model tries to maximize the width of the margin between classes using a nonlinear class boundary.
    • Tuning parameters:
      • cost: A positive number for the cost of predicting a sample within or on the wrong side of the margin
      • degree: A positive number for polynomial degree
      • scale_factor: A positive number for the polynomial scaling factor
  • SVM Radial Model: The model tries to maximize the width of the margin between classes using a polynomial class boundary.
    • Tuning parameters:
      • cost: A positive number for the cost of predicting a sample within or on the wrong side of the margin
      • rbf_sigma: A positive number for radial basis function
  • Multilayer Perceptron Model: A neural network where the mapping between inputs and output is non-linear
    • Tuning parameters:
      • hidden_units: An integer for the number of units in the hidden model
      • penalty: A non-negative numeric value for the amount of weight decay
  • MARS Model: A model that uses an algorithm that involves finding a set of simple linear functions to predict complex non-linear problems
    • Tuning parameters:
      • num_terms: The number of features that will be retained in the final model, including the intercept
      • prod_degree: The highest possible interaction degree

Assessment Measures

We will use roc_auc as our performance metric for model performance. Once we have picked our final model and fitted it to our testing set, we will look atroc_auc, accuracy, and visualize a confusion matrix as well.

  • Accuracy: accuracy measures the proportion of correctly classified predictions over the total number of predictions

  • ROC_AUC: a roc_auc curve measures the probability that any randomly identified positive prediction is ranked higher by the model than a randomly identified negative prediction. It produces an overall evaluation of the model’s performance

  • Confusion Matrix: a confusion matrix is used to create a table that summarizes the predictions made in a classification model. It identifies the number of true positives, true negatives, false positives, and false negatives.

Model Performance

Displayed below is a graph of model results.

As said before, the long recipes have 10 folds and 5 repeats, and are performed on the training set of 26971. The short recipes have 5 folds and 3 repeats, and are performed on a portion of the training set of 4045 variables. However, the short recipe for the random forest importance recipe has 5 folds and 3 repeats and is performed on the entire training set.

We tuned a random forest model with the importance recipe, as the random forest model with the kitchen sink recipe had the lowest roc_auc. The random forest with the importance recipe performed slightly worse than the random forest with the kitchen sink recipe.

model roc_auc recipe_type runtime
Boosted Tree: KS Recipe 0.6844175 short 1514.802
Boosted Tree: Relationship Recipe 0.6539740 long 118542.876
Elastic Net: KS Recipe 0.6562386 long 2579.432
KNN: KS Recipe 0.5766798 long 7142.935
KNN: Relationship Recipe 0.6005303 long 1645.249
Logistic Regression: KS Recipe 0.6321620 short 188.730
Logistic Regression: Relationship Recipe 0.6212871 long 369.249
MARS: KS Recipe 0.6637773 long 896.524
MARS: Relationship Recipe 0.6273647 long 166.730
Neural Network: KS Recipe 0.6745134 short 7750.394
Neural Network: Relationship Recipe 0.6109543 short 1717.030
Null 0.5000000 n/a 36.183
Random Forest: Importance Recipe 0.7118707 short 29048.241
Random Forest: KS Recipe 0.7139184 long 98108.910
Random Forest: Relationship Recipe 0.6436749 long 46831.557
SVM Poly: KS Recipe 0.6350800 short 20251.528
SVM Poly: Relationship Recipe 0.5848137 short 5997.018
SVM Radial: KS Recipe 0.6350800 short 6208.302
SVM Radial: Relationship Recipe 0.5847879 short 1406.635

Next, we will visualize the best performing models. We will be doing this with all of the models that had an roc_auc over 0.65.

Kitchen Sink Recipe (long)

Kitchen Sink Recipe (short)

Relationship Recipe

Importance Recipe

All of the models have small confidence intervals, except the neural network with the shortened kitchen sink recipe and the random forest with the importance recipe.

Tuning Parameters

We tuned at fit 9 models in our exploration. Aside from the null model, we added additional parameters to our other models to further improve their performance. Each of these graphs shows the roc_auc curve for each model in both the kitchen sink nd relationship recipes.

As mentioned in the Assessment Measures section, the roc_auc curve provides a visual representation of the relationship between the true positive rate (sensitivity) and the false positive rate (1-specificity).

Here are the graphs for each model:

Kitchen Sink Recipe

  • Random Forest Model:

In this model, the peak of the curve moves towards the top-left corner, which indicates that this model has a relatively low rate of falsely identifying negative cases as positive. Also, the peak of the curve is approaching the upper-left corner, which means this model has a higher proportion of actual positive cases that were correctly classified as positive. These results show that this model is proficient in its predictions and performs well.

For this model, it seems that it has the best roc_auc score as the number of randomly selected predictors increases. A higher minimal node score seems to improve the roc_auc score as well.

  • Boosted Tree Model:

This model looks very similar to the random forest model, and produces the same advantages as that model. This model performs best with a higher number of predictors and a smaller minimal node size.

  • K Nearest Neighbors Model:

This model performs best with a higher number of neighbors. This also means when its performing its best, it can take into account a larger number of data points from different classes, but this also means it may be more robust and could lose information for some of the smaller details.

  • Elastic Net Model:

This model has the best roc_auc score when it has lower levels of regularization. Regularization is a method that is used to prevent overfitting. At it’s best, this model has low regularization, which means means the model is less restricted, which can cause overfitting.

  • Logistic Regression Model:

This graph looks very similar to the previous one. It indicates that this model has high a higher roc_auc score with lower regularization but is relatively bad at avoiding overfitting.

  • MARS Model:

This model has the best roc_auc score as the number of model terms increases. The model terms refer to the individual functions that make up the MARS model, so in this case, the more components the MARS model has, the better its roc_auc performance will be.

  • Multilayer Perceptron Model:

This model performance varies as the amount of regularization changes. There is not a clear trend of what amount of regularization leads to a higher roc_auc score.

In general, it seems that the model performs better with a lower of hidden units, which means it has a less complex model structure with less patterns and representations.

  • SVM Poly Model:

The SVM Poly Model contains different degrees of interaction. Each of these degrees refers to the polynomial degree that is used in the kernel function. The kernel function determines how the data is transformed and separated in a higher-dimensional feature space. Degree 1 is a linear kernel, degree 2 is a quadratic kernel, and degree 3 is a higher-degree polynomial kernel.

These graphs also test the cost parameter. The cost parameter determines the penalty for incorrectly classifying training examples, and influences the width and number of support vectors in an SVM Poly Model.

In each of these graphs, the results vary heavily among each of the scale factors, with the higher scale factors performing better. Generally, cost does not seem to affect the roc_auc score. This means that although this model can perform well, it’s overall roc_auc score is relatively low.

  • SVM Radial Model:

In an SVM Radial model, the radial basis function parameter sigma determines the width of the kernel that is used to transform the data into a higher-dimensional feature space.

This model performs similarly to the previous one in that the results are quite varied among each radial basis function sigma. This means that overall, the model has relatively low performance when tested using the roc_auc metric, and has varied widths with each kernel. The cost does not seem to affect the roc_auc score.

Relationship Recipe

  • Random Forest Model:

For the random forest model with the relationship recipe, it seems that the random forest model has the best roc_auc score when it has around 5 randomly selected predictors. When this occurs, the roc_auc score for this model is relatively high, but otherwise, it doesn’t perform as well.

  • Boosted Tree Model:

The boosted tree model with the relationship recipe has the best roc_auc score as the number of randomly selected predictors increases. Smaller minimum node size seems to improve the roc_auc score. The learning rate does not seem to affect thr roc_auc score.

  • K Nearest Neighbors Model:

The KNN model with the relationship recipe has a higher roc_auc score as the number of neighbors increases.

  • Elastic Net Model:

The elastic net model has the best roc_auc score when the amount of regularization is around 1e-03. Generally, a range of 0 to 1e-03 leads to a higher roc_auc score. In this range, the roc_auc score is highest, and the amount of regularization means the model is relatively more proficient at preventing overfitting.

  • Logistic Regression Model:

This model performs similarly to the previous on with the highest roc_auc score occurring when the amount of regularization remains between 0 and 1e-03.

  • MARS Model:

For both degrees of interaction, this model has the highest roc_auc score as the number of model terms increases. 2 degrees of intereaction also lead to a higher roc_auc score.

  • Multilayer Perceptron Model:

Depending on the amount of regularization, this model has varying degrees of roc_auc performance. A lower number of hidden unit generally lead to a higher roc_auc score. However, because these results are so varied, it shows that the overall performance of this model is relatively poor.

  • SVM Poly Model:

A higher scale factor seems to lead to a higher roc_auc score. There is not a clear pattern in cost. The degrees of interaction do not seem to heavily impact the roc_auc score.

  • SVM Radial Model:

This model is varied in its roc_auc score for each radial basis function sigma. There is also not a clear trend with cost in its impact on the roc_auc score.

Importance Recipe

  • Random Forest Model:

For the random forest model with the importance recipe, as the number of randomly selected predictors increases, the roc_auc score increases. As the minimal node size increases, the roc_auc score also increases.

Takeaway

After examining all of the different models, it seems that the random forest model had the best overall performance with the roc_auc score. This means it has the best balance between correctly identifying positive cases and avoiding false positive cases. When plotted using the importance recipe, the random forest model still performs very well in both of these areas, further affirming that this is model has the best overall performance.

Final Model Selection

Overall, the tree methods seemed to perform the best on this dataset with the random forest and boosted tree models producing the best results. Also, the kitchen sink recipe did better than the relationship recipe, implying that the benefits of more predictors used outweighed the benefits of only using the predictors that displayed relationships with the outcome variable. The importance recipe combined the two, by using more predictors than the relationship recipe and only using variables with predictive importance. However, in the end, the kitchen sink recipe did slightly better than the importance recipe with the random forest model. We think that this may be due to the importance recipe using fewer folds and repeats to shorten the runtime.

We expected the svm models to do better than they did. We believe that the reasoning behind the svm performing worse than expected is also due to the need to use fewer folds and repeats and to cut down the training set. When we originally ran the svm models, the models were running for over 48 hours. So, we decided to cut down the number of folds and repeats and the recipe to save runtime.

The final model we will use is the random forest with the kitchen sink recipe. We are not surprised, as random forest models do well in managing outliers and in preventing overfitting. Also, as mentioned before, the tree method seems to do well in predicting is_exchangeable. However, we are surprised that the kitchen sink recipe performed better than the importance recipe. Again, it is likely due to the number folds and repeats used for each recipe and model.

Final Model Analysis

Now that we have chosen our best model, we will complete our final model workflow and fit it to the testing data.

Class probabilities are an estimation of the probability that an observation belongs to each class for is_exchangeable (TRUE or FALSE) in a set of classes (TRUE and FALSE).

So, .pred_TRUE = 0.51 and .pred_FALSE = 0.49 would imply that our model had trouble classifying the car, whereas .pred_TRUE = 0.95 and .pred_FALSE = 0.05 would imply that my model confidently classified a car as being exchangeable.

The table below shows the observations of is_exchangeable in the testing data and compares it to what the final model predicted its is_exchangeable value would be.

is_exchangeable prediction .pred_FALSE .pred_TRUE
TRUE TRUE 0.3522711 0.6477289
TRUE FALSE 0.5009135 0.4990865
TRUE TRUE 0.3018301 0.6981699
FALSE FALSE 0.5208096 0.4791904
FALSE TRUE 0.4577452 0.5422548
TRUE FALSE 0.5208880 0.4791120
FALSE FALSE 0.5050616 0.4949384
FALSE FALSE 0.6669565 0.3330435
FALSE FALSE 0.5841697 0.4158303
FALSE FALSE 0.5523678 0.4476322
TRUE FALSE 0.5568756 0.4431244
TRUE TRUE 0.4954581 0.5045419
FALSE FALSE 0.5765153 0.4234847
FALSE TRUE 0.3647457 0.6352543
TRUE FALSE 0.5401406 0.4598594
FALSE FALSE 0.6208666 0.3791334
FALSE FALSE 0.7021177 0.2978823
FALSE FALSE 0.5228514 0.4771486
FALSE FALSE 0.6229149 0.3770851
TRUE FALSE 0.5164900 0.4835100
FALSE FALSE 0.5852798 0.4147202
TRUE FALSE 0.5543870 0.4456130
TRUE FALSE 0.5466917 0.4533083
TRUE TRUE 0.4032182 0.5967818
FALSE TRUE 0.4936109 0.5063891
FALSE FALSE 0.5954138 0.4045862
FALSE FALSE 0.6010178 0.3989822
TRUE FALSE 0.5120790 0.4879210
FALSE FALSE 0.6762732 0.3237268
FALSE FALSE 0.7194945 0.2805055
TRUE TRUE 0.4457545 0.5542455
FALSE FALSE 0.5108102 0.4891898
TRUE FALSE 0.6837317 0.3162683
TRUE FALSE 0.6498809 0.3501191
TRUE FALSE 0.5647539 0.4352461
FALSE FALSE 0.6351073 0.3648927
TRUE FALSE 0.5754936 0.4245064
FALSE FALSE 0.6635704 0.3364296
TRUE FALSE 0.5541341 0.4458659
FALSE FALSE 0.6337017 0.3662983
FALSE FALSE 0.7033620 0.2966380
FALSE FALSE 0.6755714 0.3244286
TRUE FALSE 0.5120742 0.4879258
TRUE TRUE 0.2333058 0.7666942
TRUE FALSE 0.7017623 0.2982377
FALSE FALSE 0.6295448 0.3704552
TRUE FALSE 0.5761142 0.4238858
FALSE FALSE 0.5651437 0.4348563
FALSE FALSE 0.5777452 0.4222548
TRUE FALSE 0.5639720 0.4360280
TRUE FALSE 0.6453087 0.3546913
FALSE FALSE 0.7759943 0.2240057
TRUE FALSE 0.6903960 0.3096040
TRUE FALSE 0.5417950 0.4582050
TRUE FALSE 0.7825488 0.2174512
FALSE TRUE 0.4647199 0.5352801
FALSE FALSE 0.6766829 0.3233171
TRUE FALSE 0.5278442 0.4721558
TRUE FALSE 0.5570423 0.4429577
FALSE FALSE 0.7278323 0.2721677
FALSE FALSE 0.6968686 0.3031314
FALSE FALSE 0.7155484 0.2844516
FALSE FALSE 0.7849011 0.2150989
FALSE FALSE 0.7776628 0.2223372
FALSE TRUE 0.4033136 0.5966864
FALSE FALSE 0.8328875 0.1671125
TRUE FALSE 0.6647930 0.3352070
FALSE FALSE 0.7101221 0.2898779
FALSE FALSE 0.7058990 0.2941010
FALSE FALSE 0.5204085 0.4795915
TRUE FALSE 0.6659469 0.3340531
FALSE FALSE 0.7877926 0.2122074
FALSE FALSE 0.6754748 0.3245252
FALSE FALSE 0.8576733 0.1423267
TRUE FALSE 0.6268306 0.3731694
FALSE FALSE 0.7425773 0.2574227
FALSE FALSE 0.8681795 0.1318205
FALSE FALSE 0.7890946 0.2109054
FALSE FALSE 0.7515394 0.2484606
FALSE FALSE 0.8644329 0.1355671
FALSE FALSE 0.6369573 0.3630427
FALSE FALSE 0.7332810 0.2667190
FALSE FALSE 0.7148189 0.2851811
FALSE FALSE 0.7670500 0.2329500
FALSE FALSE 0.5570571 0.4429429
TRUE TRUE 0.4568455 0.5431545
TRUE FALSE 0.8212561 0.1787439
TRUE TRUE 0.3105502 0.6894498
FALSE FALSE 0.7219720 0.2780280
FALSE FALSE 0.7218763 0.2781237
FALSE FALSE 0.7467210 0.2532790
FALSE FALSE 0.7405905 0.2594095
FALSE TRUE 0.3312903 0.6687097
FALSE FALSE 0.5670521 0.4329479
FALSE FALSE 0.6240614 0.3759386
TRUE FALSE 0.5360867 0.4639133
FALSE FALSE 0.6541453 0.3458547
TRUE FALSE 0.7961618 0.2038382
FALSE FALSE 0.7919417 0.2080583
FALSE FALSE 0.7770491 0.2229509
TRUE FALSE 0.7637182 0.2362818
FALSE FALSE 0.7919931 0.2080069
FALSE FALSE 0.8355194 0.1644806
TRUE FALSE 0.5447703 0.4552297
FALSE TRUE 0.4299420 0.5700580
TRUE FALSE 0.6042209 0.3957791
FALSE FALSE 0.8767898 0.1232102
FALSE FALSE 0.6058006 0.3941994
FALSE FALSE 0.6886365 0.3113635
FALSE FALSE 0.8633819 0.1366181
FALSE FALSE 0.8417804 0.1582196
FALSE FALSE 0.9060569 0.0939431
FALSE FALSE 0.8605720 0.1394280
FALSE FALSE 0.6911205 0.3088795
FALSE FALSE 0.8273724 0.1726276
FALSE FALSE 0.8821442 0.1178558
FALSE FALSE 0.7002586 0.2997414
FALSE FALSE 0.8677568 0.1322432
TRUE FALSE 0.8068316 0.1931684
FALSE FALSE 0.6979823 0.3020177
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FALSE TRUE 0.4643924 0.5356076
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ROC Curve

The ROC curve shows the trade-off between sensitivity (or true positive rate) and specificity (1 – true positive rate). In this case, the true positive observation would be is_exchangeable = FALSE. The true positive rate is the proportion of observations that were correctly predicted to be positive out of all positive observations.

The closer to the top left corner the curve is, the better the model performance. As a baseline, a null model is expected to give points lying along the dotted diagonal line. So, it seems that our model did significantly better than the null model.

Area Under ROC Curve

The area under the ROC curve of our final model is the probability that the model correctly classifies a car that is exchangeable from a car that isn’t. It provides an aggregate measure of performance across all possible classification thresholds. A value of 0.715 means that our random forest model with the kitchen sink recipe did pretty well in correctly classifying the cars in the testing set, though there is still some room for error. It performed similarly on the testing set as it did in the training set.

.metric .estimator .estimate
roc_auc binary 0.7151476

Accuracy

Our final model was able to accurately predict 70.17% of the observations in our testing set. This means that my model was able to correctly predict whether a car was exchangeable or not for 8111 out of the 11560 cars in the testing set.

.metric .estimator .estimate
accuracy binary 0.7017301

Confusion Matrix

The confusion matrix shows how accurate our final model predictions are. So, in the (Prediction FALSE, Truth FALSE) category, these are the amount of observations that we correctly predicted were FALSE. In the (Prediction FALSE, Truth TRUE) category, these are the amount of observations that we incorrectly predicted were FALSE. In the (Prediction TRUE, Truth FALSE), these are the amount of observations that Iwe incorrectly predicted were TRUE. In the (Prediction TRUE, Truth TRUE), these are the amount of observations that we correctly predicted were TRUE. Essentially, it is a visual representation of the performance metric accuracy.

We see that our final model did better at predicting the cars that were not exchangeable than predicting cars that were. It correctly classified 90.61% of the cars that were not exchangeable, and only 67.35% of the cars that were exchangeable. This issue can be partially attributed to the imbalance of is_exchangeable, as there were around 2x more FALSE observations than TRUE.

          Truth
Prediction FALSE TRUE
     FALSE  6781 2745
     TRUE    703 1331

Comparing Final Model to Null Model

model metric mean
Null ROC 0.5
Null Accuracy 0.647399053886577
RF ROC 0.7151476
RF Accuracy 0.7017301

Our final model did better than the null model when comparing their area under the ROC curve, but not as well when comparing their accuracy. When comparing their accuracy, our final model performed similarly to the null model. Overall, accuracy is based on one specific cutpoint, while ROC tries all of the cutpoint and plots and the sensitivity and specificity. So when we compare the overall accuracy, we are comparing the accuracy based on a designated cutpoint. The overall accuracy varies from different cutpoints. Therefore, our final model’s accuracy being worse than its area under the ROC curve may be due to choosing a cutpoint that yields a lower accuracy.

Overall, our final model did significantly better than the null model, so we think it is worth the effort of building a predictive model. However, the runtime is very long, so we would need find ways to shorten the runtime. In shortening the runtime, we need to be careful to not worsen model performance, as uing fewer folds and repeats or shortening the training set can cause model predictions to be less accurate.

Conclusion

In conclusion, the final model performed well but did not fit our purposes to determine what variables make a car exchangeable. Our final model was a kitchen sink model that used all of the variables as predictors. Our relationship recipe that used graph variable selection methods had relatively poor model performance. The importance recipe performed slightly worse with the random forest model. This may have been due to the random forest with the importance recipe using fewer folds and repeats than the random forest model with the kitchen sink recipe.

Our next steps are to run the importance recipe on the rest of the models. We will then adjust tuning parameters based on the trends that we observed that led to higher roc_auc. Overall, we think that we need more variables in the dataset to choose from, as there are only 20 right now. In having more variables, we think our variable selection methods will be more successful, as the benefit of the KS model using more predictors is not as important. We will then be able to look at what factors make a car exchangeable.

References

Kirill Lepchenkov (2019, December 2). Used Cars Catalog. Kaggle. https://www.kaggle.com/datasets/lepchenkov/usedcarscatalog